Remark 3.5.7.21. Let $f: X \rightarrow Y$ be a morphism of Kan complexes. The condition that $f$ exhibits $Y$ as an $n$-truncation of $X$ depends only on the homotopy class $[f]$ (see Remark 3.5.1.20).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Remark 3.5.7.21. Let $f: X \rightarrow Y$ be a morphism of Kan complexes. The condition that $f$ exhibits $Y$ as an $n$-truncation of $X$ depends only on the homotopy class $[f]$ (see Remark 3.5.1.20).